Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#14555772 | C2 | semidirect |
| 3. C2×#17984849 | C2 | semidirect |
| 4. #22581218 | C2 | direct (N × H) |
| 5. C2×#17984777 | C2 | semidirect |
| 6. C2×#17984761 | C2 | semidirect |
| 7. C2×#17984758 | C2 | semidirect |
| 8. C2×#137×C139 | C2 | semidirect |
| 16. C2×#14555772 | C22 | semidirect |
| 19. #17984849 | C22 | semidirect |
| 25. #17984777 | C22 | semidirect |
| 26. #17984761 | C22 | semidirect |
| 27. #17984758 | C22 | semidirect |
| 31. #137×C139 | C22 | semidirect |
| 135. C2×C139 | #471 | semidirect |
| 138. C139 | C2×#471 | semidirect |
| 140. C2×#137 | D139 | semidirect |
| 152. #137 | C2×D139 | semidirect |
| 275. C2 | #22581218 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984867 | 2 |
| C22×#14555772 | 2 |
| C2×#17984849 | 2 |
| #22581218 | 2 |
| C2×#17984777 | 2 |
| C2×#17984761 | 2 |
| C2×#17984758 | 2 |
| C2×#137×C139 | 2 |
| C2×#471 | 139 |